SOLUTION: a) A city has four fire engines. For each fire engine the probability that it is available is 0.9. A fire accident happens somewhere in the city one Thursday afternoon. It is deter
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Question 1183439: a) A city has four fire engines. For each fire engine the probability that it is available is 0.9. A fire accident happens somewhere in the city one Thursday afternoon. It is determined that fire engines will be needed:
(i) What is the chance that exactly 2 engines are available?
(ii) What is the probability that at least two of the engines are available?
(iii) What is the chance that none of the engines are available?
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A city has four fire engines. For each fire engine the probability that it is available is 0.9.
A fire accident happens somewhere in the city one Thursday afternoon.
It is determined that fire engines will be needed:
(i) What is the chance that exactly 2 engines are available?
(ii) What is the probability that at least two of the engines are available?
(iii) What is the chance that none of the engines are available?
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All three problems are the binomial distribution type of problems.
(i) The number of trials n= 4; the probability of the success trial is 0.9, and the number of success trials k = 2.
P = = = 0.0486 (rounded). ANSWER
(ii) The number of trials n= 4; the probability of the success trial is 0.9, and the number of success trials k >= 2.
We need calculate P(n=4; k>=2; p=0.9).
To facilitate calculations, I use an appropriate online (free of charge) calculator at this web-site
https://stattrek.com/online-calculator/binomial.aspx
It provides nice instructions and a convenient input and output for all relevant options/cases.
P(n=4; k>=2; p=0.9) = 0.9963 (rounded). ANSWER
(iii) This probability is
P = = = 0.0001. ANSWER
Solved. // All questions are answered and explained.